1. Field of the Invention
The invention concerns a method for filtered back-projection of a projection image data set. The invention furthermore concerns a device and a non-transitory, computer-readable storage medium to implement the method.
2. Description of the Prior Art
In typical medical and non-medical methods (for example computed tomography) a projection image data set is used as an intermediate product in order to reconstruct, via back-projection, the three-dimensional, internal structure of an imaged subject. In the medical application, the subject is normally a body part of a patient.
The projection image data set is a series of projection images of the subject that were acquired at different projection angles in an image plane situated opposite the projection origin.
Computed tomography and similar imaging methods (for example rotation angiography) are x-ray acquisition methods. In these methods, an x-ray radiator is arranged in the projection origin, and the x-ray radiator radiates an x-ray beam through the subject to be examined onto an x-ray detector arranged in the image plane. In modern variants of computed tomography or rotation angiography, a conical x-ray beam (cone beam) is normally emitted by the x-ray radiator. The radiation transmitted through the subject is detected in two dimensions with spatial resolution at the detector.
The Feldkamp algorithm or the Clack-Defrise algorithm are conventionally used for the reconstruction of a projection image data set acquired in cone beam geometry. Both algorithms follow a common scheme; the projection image data set is consequently initially filtered and is subsequently projected back.
The Feldkamp algorithm is relatively uncomplicated mathematically and thus can be implemented quickly with simple means. However, it disadvantageously leads to significant image artifacts (shadows, for example) in the reconstructed 3D image data (tomogram) of the examined subject, in particular given acquisitions along only a portion of a circle, with a scan angle of less than 360°.
The Clack-Defrise algorithm is mathematically significantly more complicated than the Feldkamp algorithm; but it enables a significantly higher precision of the resulting 3D image data as a result of two-dimensional filter operations and due to a theoretically exact treatment of data redundancies.
However, it is common to both algorithms to take a weighting factor into account in the back-projection step, this weighting factor being inversely proportional to the quadratic interval (measured in the direction of a central beam of the cone beam geometry) of the projection origin relative to the spatial point (back-projection location) to be reconstructed. This weighting factor is also designated as a “back-projection weight”.
The back-projection weight disadvantageously has a negative influence on the image quality because that it leads to an anisotropic spatial resolution in the resulting tomogram, as well as to a non-uniform distribution of the image noise; see F. Dennerlein, et al.: “Fan-beam filtered-backprojection reconstruction without backprotection weight”, Phys. Med. Biol. 52(11):3227-3239, 2007; G. L. Zeng.: “Nonuniform noise propagation by using the ramp filter in fan-beam computed tomography”, IEEE Trans. Med. Imag. 23(6):690-695, 2004).
From Dennerlein et al.: “Filtered backprojection reconstruction with depth-dependent filtering”, Tsinghua Science+Technology, 15(1):17-24, 2010, a method is known by means of which the back-projection weight is eliminated, and thus the image noise and the spatial resolution can be homogenized. This method is applicable without further measures to the Feldkamp algorithm but not to the Clack-Defrise algorithm. Given application to the later, the back-projection weight—and the disadvantages connected therewith—must therefore continue to be accepted.
An object of the invention is to enable a back-projection of a projection image data set acquired in a cone beam geometry, wherein the back-projection is particularly precise, low in artifacts, and homogeneous.